An object is subjected to a force in the north-east direction. To balance this force,a second force should be applied in the direction:

If $0.5 \hat{i} + 0.8 \hat{j} + c \hat{k}$ is a unit vector,then $c$ is

State with reasons,whether the following algebraic operations with scalar and vector physical quantities are meaningful:
$(a)$ adding any two scalars,
$(b)$ adding a scalar to a vector of the same dimensions,
$(c)$ multiplying any vector by any scalar,
$(d)$ multiplying any two scalars,
$(e)$ adding any two vectors,
$(f)$ adding a component of a vector to the same vector.

If $|\vec A + \vec B| = |\vec A| + |\vec B|$,then the angle between $\vec A$ and $\vec B$ will be ....... $^o$.

Which of the following quantity/quantities are dependent on the choice of orientation of the co-ordinate axes?
$(a)$ $\vec{a}+\vec{b}$
$(b)$ $3a_x+2b_y$
$(c)$ $(\vec{a}+\vec{b}-\vec{c})$

The component of a vector $P=3 \hat{i}+4 \hat{j}$ along the direction $(\hat{i}+2 \hat{j})$ is